Superconducting contact and quantum interference between two-dimensional van der Waals and three-dimensional conventional superconductors

This paper is a contribution to the joint Physical Review Applied and Physical Review Materials collection titled Two-Dimensional Materials and Devices.

Atomically thin two-dimensional (2D) transition-metal dichalcogenide (TMD) superconductors enable uniform, flat, and clean van der Waals tunneling interfaces, motivating their integration into conventional superconducting circuits. However, fully superconducting contact must be made between the 2D material and three-dimensional (3D) superconductors to employ the standard microwave drive and readout of qubits in such circuits. We present a method for creating zero-resistance contacts between 2D ${\mathrm{NbSe}}_2$ and 3D aluminum that behave as Josephson junctions (JJs) with large effective areas compared to 3D-3D JJs. The devices formed from 2D TMD superconductors are strongly influenced by the geometry of the flakes themselves as well as the placement of the contacts to bulk 3D superconducting leads. We present a model for the supercurrent flow in a 2D-3D superconducting structure by a numerical solution of the Ginzburg-Landau equations and find good agreement with experiment. These results demonstrate a crucial step towards a new generation of hybrid superconducting quantum circuits.

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Figure 1

Contact method and cross-sectional transmission electron microscopy (TEM). (a) Contact method. Thin ${\mathrm{NbSe}}_2$ is encapsulated by hBN. A reactive-ion etch exposes the ${\mathrm{NbSe}}_2$ edge. Following an in situ argon ion mill, contact is made using angled evaporation of aluminum with no adhesion layer. (b) Cross-sectional TEM of ${\mathrm{NbSe}}_2$-Al interface in device F. (c) False-color energy dispersive spectroscopy (EDS) map of the ${\mathrm{NbSe}}_2$-Al contact in device G. A slight delamination of the top hBN near the contact is visible, as in (b). Minimal oxygen is observed at the ${\mathrm{NbSe}}_2$-Al contact.

Figure 2

Zero-resistance contact between few-layer ${\mathrm{NbSe}}_2$ and aluminum. (a) $R\left(T\right)$ for Al-${\mathrm{NbSe}}_2$-Al device F. Inset (bottom right): Linear plot of $R\left(T\right)$ showing the Al and two ${\mathrm{NbSe}}_2$ transitions. Inset (top left): Four-point measurement setup for measuring the contact resistances of the Al/${\mathrm{NbSe}}_2$ contacts. (b) Differential resistance ($dV/dI$) vs dc current $I_{\mathrm{dc}}$ of device F, showing four dc critical currents. All measurements are filtered with low-pass and rf filters (Appendix pp3).

Figure 3

Quantum interference in a two-terminal ${\mathrm{NbSe}}_2$-aluminum device. (a) Model of a 3D-3D Josephson junction. The phase difference $\mathrm{\Delta }\varphi$ across the junction depends on the $z$ coordinate. $\mathrm{\Delta }{\varphi }_{P{P}^{\prime }}-\mathrm{\Delta }{\varphi }_{Q{Q}^{\prime }}$ changes by $2\pi$ when one ${\mathrm{\Phi }}_0$ of flux is threaded through the area depicted in magenta. (b) Model of a 2D-3D JJ. In response to a field B, circulating supercurrent ${\mathbf{J}}_{\mathbf{s}}$ (blue arrows) flows in the 2D bulk. The phase difference across the junction winds by $2\pi$ from point $P$ to point $Q$ when one ${\mathrm{\Phi }}_0$ is threaded through the effective area of the 2D-3D junction. This requires the effective area to be bounded by a contour of constant phase in the interior of the 2D flake, $\overline{POQ}$, perpendicular to ${\mathbf{J}}_{\mathbf{s}}$ everywhere. (c) Scanning electron microscopy (SEM) image of device F. (d) $dV/dI$ as a function of $I_{\mathrm{dc}}$ and $B$ for device F. Two superimposed single-junction critical current vs field $I_c\left(B\right)$ responses are visible. Theoretical $I_c\left(B\right)$ curves (black dotted and dashed lines) generated from the numerical simulations shown in E and F are overlaid on the data. Data for $I_{\mathrm{dc}}<50\mu \mathrm{A}$ were acquired at 100 mK; slight heating occurs above $50\mu \mathrm{A}$ but does not affect the analysis (Fig. 6). (e) Calculated supercurrent distribution ${\mathbf{J}}_{\mathbf{s}}$ and (f) effective areas $A_L$ and $A_R$ associated with the left and right contacts.

Figure 4

Quantum interference in a 2D-3D ${\mathrm{NbSe}}_2$-aluminum SQUID. (a) Optical micrograph of device C. $dV/dI$ measurements are performed between contacts No. 3 and No. 4 while contacts No. 1 and No. 2 are floating. Outline of ${\mathrm{NbSe}}_2$ flake is shown in dashed purple line. (b) Quantum interference pattern observed in device C. A minimum resistance of ${(dV/dI)}_{\min }=81\mathrm{\Omega }$ has been subtracted from the data. Data for SQUID device B (Fig. S5 [23]) show a true zero resistance as $T\to 0$. Inset: Fast Fourier transform (FFT) amplitude of a linecut along $I_{\mathrm{dc}}=0$ (the following results do not depend on chosen $I_{\mathrm{dc}}=0$). The three frequencies, indicated by arrows, are $1/\mathrm{\Delta }{B}_i=2.7$, 6.8, and $9.5{\mathrm{mT}}^{-1}$ (corresponding respectively to periods $\mathrm{\Delta }{B}_i=0.37$, 0.15, and 0.11 mT, shown as black scale bars in the main figure, and areas $A_{\mathrm{meas}}^{\left(i\right)}={\mathrm{\Phi }}_0/\mathrm{\Delta }{B}_i=5.4$, 13.6, and $19.1\mu {\mathrm{m}}^2$). The lowest and highest of these areas match the calculated effective areas of the SQUID source and 2D-3D drain contacts. (c) SEM image of the SQUID “source” contact in device C formed by two Al contacts to the ${\mathrm{NbSe}}_2$ flake. (d) In a 3D-3D SQUID, the supercurrent ${\mathbf{J}}_{\mathbf{s}}$ flows in a surface layer of depth $\sim \lambda$. The fluxoid quantization contour $C$ can be chosen deep in the interior of the superconductor such that ${\int }_C{\mathbf{J}}_{\mathbf{s}}·\mathbf{d}\ell =0$. (e) In a 2D-3D SQUID, since ${\mathbf{J}}_{\mathbf{s}}$ is nonzero everywhere in the 2D layer, $C$ must be a contour of constant phase inside the bulk, which results in a larger effective area determining the periodicity of $I_c\left(B\right)$ oscillations.

Figure 5

(a) After the lithographic mask is patterned via electron-beam lithography (EBL), a reactive-ion etch is used to expose a cross section of the hBN/${\mathrm{NbSe}}_2$/hBN heterostructure. The stack is then loaded into a Plassys 8-pocket e-gun evaporator with an ion gun where a 3-min Ar ion mill step is used to expose a fresh facet in situ before evaporation. (b) Aluminum is evaporated at an angle ${30}^{\circ }$ from vertical. (c) Optionally, additional evaporation angles can be used, but will result in additional aluminum critical currents due to the layering [see Figs. S4(b) and S4(c) 23].

Figure 6

Comparison of $R\left(T\right)$ plots of devices A and B measured with filters, and device J (not listed in Table S1) without any filters used in the measurement. The curve from Fig. S4(a) is reproduced and compared with a measurement on the same device using only rf filters with a cutoff frequency in the GHz regime. $R\left(T\right)$ for the SQUID device B with all filters in place shows a residual resistance two orders of magnitude lower than that of device J without filters, but unlike device A, the resistance remains nonzero.

Figure 7

(a) $dV/dI$ vs $T$ and $I_{\mathrm{dc}}$ at 0 mT (device F). The critical currents associated with the contacts ($I_c^{\left(1\right)}$ and $I_c^{\left(2\right)}$) are well below their maximum at zero flux, indicating that this measurement with zero applied field is measuring a finite amount of trapped flux through the ${\mathrm{NbSe}}_2$ flake in the areas associated with each junction. (b) $dV/dI$ vs $T$ and $I_{\mathrm{dc}}$ at 3 mT. The smaller of the critical currents (associated with the narrower of the two contacts) exhibits hopping behavior between two discrete flux states. This suggests that a single vortex is moving in and out of the area of the ${\mathrm{NbSe}}_2$ flake measured by this contact. The shift in $I_c$ between the two levels is significant. In both plots, the $T_c$ of all critical currents associated with the aluminum leads and Al/${\mathrm{NbSe}}_2$ contacts is 1.2 K. Above 5.5 K the ${\mathrm{NbSe}}_2$ critical current splits into two critical currents with $T_c=6.5$ and 7 K. Note: The discontinuity in $I_c^{\left(4\right)}$ (${\mathrm{NbSe}}_2$) at 4 K is attributed to the different heating behavior of the cryogen-free dilution refrigerator above and below 4 K, and the positive slope of the color plots' lower boundaries show the inaccessible temperature region due to Joule heating at larger $I_{\text{dc}}$ values.

Figure 8

STEM images of the contacts for devices F/G and false-color EDS and HAADF maps of device G used to produce Figs. 1 and 1(c). (a) $56.5\mu \mathrm{A}$ and (b) $78.5\mu \mathrm{A}$ critical current contacts of device F. (c) $128\mu \mathrm{A}$ and (d) $108\mu \mathrm{A}$ critical current contacts of device G. (e), (f) Detailed images of the Al/${\mathrm{NbSe}}_2$ contact regions of device G. (g) Composite EDS $+$ HAADF map. Scale bar is 100 nm and is the same for all subfigures. (h) HAADF. (i)–(n) EDS maps of (i) nitrogen, (j) niobium, (k) oxygen, (l) selenium, (m) silicon, and (n) aluminum.